Evariste Galois

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File:Galois.jpeg
Galois at the age of fifteen from the pencil of a classmate. He was young-looking for his age and had black hair.

Évariste Galois (October 25, 1811May 31, 1832) was a French mathematician born in Bourg-la-Reine. He was a mathematical child prodigy. While still in his teens, he was able to determine a necessary and sufficient condition for a polynomial to be solvable by radicals, thereby solving a long-standing problem. His work laid the fundamental foundations for Galois theory, a major branch of abstract algebra, and the subfield of Galois connections. He was the first to use the word "group" as a technical term in mathematics to represent a group of permutations. He died in a duel at the age of twenty.

In 1828 he attempted the entrance exam to École Polytechnique, without the usual preparation in mathematics, and failed. He failed yet again on the second, final attempt the next year. It is undisputed that Galois was more than qualified; however, accounts differ on why he failed. The legend holds that he thought the exercise proposed to him by the examiner to be of no interest, and, in exasperation, he threw the rag used to clean up chalk marks on the blackboard at the examiner's head. More plausible accounts state that Galois refused to justify his statements and answer the examiner's questions. Galois's behavior was perhaps influenced by the recent suicide of his father.

His memoir on equation theory would be submitted several times but was never published in his lifetime, due to various events. Initially he sent it to Cauchy, who told him his work overlapped with recent work of Abel. Galois revised his memoir and sent it to Fourier in early 1830, upon the advice of Cauchy, to be considered for the Grand Prix of the Academy. Unfortunately, Fourier died soon after, and the memoir was lost. The prize would be awarded that year to Abel posthumously and also to Jacobi.

Despite the lost memoir, Galois published three papers that year, which laid the foundations for Galois Theory.

In January 1831, Galois returned to mathematics after a brief hiatus. Simeon Poisson asked him to submit his work on solutions of equations. Later that year, Galois would receive a letter of rejection from Poisson while in prison for his revolutionary activities. Poisson stated (to others): His argument is neither sufficiently clear nor sufficiently developed to allow us to judge its rigor.

It was resubmitted again in shorter form. The importance of the work was not generally recognized during his lifetime, although some mathematicians such as Cauchy understood its implications.

Galois was a staunch Republican, famous for having toasted Louis-Philippe with a dagger above his cup, which leads some to believe that his death in a duel was set up by the secret police. He was jailed for attending a Bastille Day protest in 1831, and was released only 2 days before his death.

The night before the duel, supposedly fought in order to defend the honor of a woman, he was so convinced of his impending death that he stayed up all night writing letters to his Republican friends and composing what would become his mathematical testament. Hermann Weyl, one of the greatest mathematicians of the 20th century, said of this testament, "This letter, if judged by the novelty and profundity of ideas it contains, is perhaps the most substantial piece of writing in the whole literature of mankind." In his final papers he outlined the rough edges of some work he had been doing in analysis and annotated a copy of the manuscript submitted to the academy and other papers. On the 30th of May 1832, early in the morning, he was shot in the abdomen and died the following day at ten in the Cochin hospital (probably of peritonitis) after refusing the offices of a priest. He was 20 years old. His last words to his brother Alfred were:

Ne pleure pas, Alfred! J'ai besoin de tout mon courage pour mourir à vingt ans!

"Don't cry, Alfred! I need all my courage to die at twenty."

Galois' mathematical contributions were finally fully published in 1843 when Liouville reviewed his manuscript and declared that he had indeed solved the problem first proposed and also solved by Abel. The manuscript was finally published in the October-November 1846 issue of the Journal des mathématiques pures et appliquées.

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